Estimation of Finite Population Mean and Total Using Conditional Inclusion Probabilities Given the Population Ranks

• Activity Number: 137
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Survey Research Methods Section
• Author(s): Omer Ozturk*
• Companies: The Ohio State University
• Keywords: Finite population ; Horwitz-Thompson estimator ; Inclusion probabilities ; Judgment post stratified sample ; Coefficient of variation ; Ranked set sampling

Abstract

This paper introduces new estimators for population total and mean in a finite population setting, where ranks of population units are available before selecting sample units. The proposed estimator selects a simple random sample and identify their ranks in the population. Selection of the sample can be performed with- or without-replacement. The population ranks of the selected units of with-replacement samples are determined among all population units. On the other hand, the ranks of the selected units of without-replacement samples are identified in two different ways: (1) The rank of a selected unit is determined sequentially among the remaining population units after excluding all previously ranked sample units from the population; (2) The ranks are determined among all units in the population. By conditioning on these population ranks, we compute the inclusion probabilities, construc three new estimators, develop a bootstrap re-sampling procedure to estimate the variances of the estimators, and construct percentile confidence intervals for the population mean and total. The new estimators provide a substantial amount of efficiency gain over their competitors.